The San Francisco Chronicle said Mr Baker died in his sleep at his home in New York on Thursday night.
He initially designed an eight-colour flag in 1978 for the city’s gay freedom day, the precursor to the modern pride parade.
The rainbow flag has been raised in central San Francisco to honour him.
It is flying near Harvey Milk Plaza, named after America’s first openly gay politician.
Mr Baker’s original flag had eight colours, each representing a different aspect of humanity:
Pink – sexuality
Red – life
Orange – healing
Green – nature
Turquoise – art
Indigo – harmony
Violet – human spirit
It would later be reduced to six stripes, removing pink and indigo, and swapping blue for turquoise.
Mr Baker said he wanted to convey the idea of diversity and inclusion, using “something from nature to represent that our sexuality is a human right”.
In 2015, New York’s Museum of Modern Art acquired the flag for its design collection, calling it a “powerful design milestone”.
“I decided that we should have a flag, that a flag fit us as a symbol, that we are a people, a tribe if you will,” Mr Baker told the Museum in an interview.
“And flags are about proclaiming power, so it’s very appropriate.”